Question

What is the sum of all positive integers lying between 200 and 400 that are multiples of 7?

Answer 1

The multiples of 7 between 200 and 400 form an A.P. where the smallest term is the multiple of 7 just greater than 200 i.e. 203 ( = 7 X 29) and the last term is the multiple of 7 just smaller than 400 i.e. 399 (= 7 X 57).

Thus, a = 203
d = 7 [ multiples of 7 differ by 7]
and, l = 399

we know that
l = a + (n-1)d
(7 X 57) = (7 X 29) + (n-1)7
57-29+1 = n
n = 29

now, required sum,

Sn = (n/2)( a + l )
= (29/2)(203+399)
= 29 X 301
= 8729

Answer 2

Answer:

refers to the attachment